The baseline intracluster entropy profile from gravitational structure formation

The radial entropy profile of the hot gas in clusters of galaxies tends to follow a power law in radius outside of the cluster core. Here we present a simple formula giving both the normalization and slope for the power-law entropy profiles of clusters that form in the absence of non-gravitational processes such as radiative cooling and subsequent feedback. It is based on seventy-one clusters drawn from four separate cosmological simulations, two using smoothed-particle hydrodynamics (SPH) and two using adaptive-mesh refinement (AMR), and can be used as a baseline for assessing the impact of non-gravitational processes on the intracluster medium outside of cluster cores. All the simulations produce clusters with self-similar structure in which the normalization of the entropy profile scales linearly with cluster temperature, and these profiles are in excellent agreement outside of 0.2 r_200. Because the observed entropy profiles of clusters do not scale linearly with temperature, our models confirm that non-gravitational processes are necessary to break the self-similarity seen in the simulations. However, the core entropy levels found by the two codes used here significantly differ, with the AMR code producing nearly twice as much entropy at the centre of a cluster.Comment: Accepted to MNRAS, 8 pages, 9 figure

Tunable Double Negative Band Structure from Non-Magnetic Coated Rods

A system of periodic poly-disperse coated nano-rods is considered. Both the coated nano-rods and host material are non-magnetic. The exterior nano-coating has a frequency dependent dielectric constant and the rod has a high dielectric constant. A negative effective magnetic permeability is generated near the Mie resonances of the rods while the coating generates a negative permittivity through a field resonance controlled by the plasma frequency of the coating and the geometry of the crystal. The explicit band structure for the system is calculated in the sub-wavelength limit. Tunable pass bands exhibiting negative group velocity are generated and correspond to simultaneously negative effective dielectric permittivity and magnetic permeability. These can be explicitly controlled by adjusting the distance between rods, the coating thickness, and rod diameters

A No-Go Theorem for Direct Collapse Black Holes Without a Strong Ultraviolet Background

Explaining the existence of supermassive black holes (SMBHs) larger than $\sim 10^9 M_\odot$ at redshifts $z >\sim 6$ remains an open theoretical question. One possibility is that gas collapsing rapidly in pristine atomic cooling halos ($T_{\rm vir} >\sim 10^4 \rm{K}$) produces $10^4-10^6 M_\odot$ black holes. Previous studies have shown that the formation of such a black hole requires a strong UV background to prevent molecular hydrogen cooling and gas fragmentation. Recently it has been proposed that a high UV background may not be required for halos that accrete material extremely rapidly or for halos where gas cooling is delayed due to a high baryon-dark matter streaming velocity. In this work, we point out that building up a halo with $T_{\rm vir} >\sim 10^4 \rm{K}$ before molecular cooling becomes efficient is not sufficient for forming a direct collapse black hole (DCBH). Though molecular hydrogen formation may be delayed, it will eventually form at high densities leading to efficient cooling and fragmentation. The only obvious way that molecular cooling could be avoided in the absence of strong UV radiation, is for gas to reach high enough density to cause collisional dissociation of molecular hydrogen ($\sim 10^4 ~ {\rm cm}^{-3}$) before cooling occurs. However, we argue that the minimum core entropy, set by the entropy of the intergalactic medium (IGM) when it decouples from the CMB, prevents this from occurring for realistic halo masses. This is confirmed by hydrodynamical cosmological simulations without radiative cooling. We explain the maximum density versus halo mass in these simulations with simple entropy arguments. The low densities found suggest that DCBH formation indeed requires a strong UV background.Comment: 5 pages, 5 figures, replaced with version accepted by MNRA

A direct N-body model of core-collapse and core oscillations

We report on the results of a direct N-body simulation of a star cluster that started with N = 200 000, comprising 195 000 single stars and 5 000 primordial binaries. The code used for the simulation includes stellar evolution, binary evolution, an external tidal field and the effects of two-body relaxation. The model cluster is evolved to 12 Gyr, losing more than 80% of its stars in the process. It reaches the end of the main core-collapse phase at 10.5 Gyr and experiences core oscillations from that point onwards -- direct numerical confirmation of this phenomenon. However, we find that after a further 1 Gyr the core oscillations are halted by the ejection of a massive binary comprised of two black holes from the core, producing a core that shows no signature of the prior core-collapse. We also show that the results of previous studies with N ranging from 500 to 100 000 scale well to this new model with larger N. In particular, the timescale to core-collapse (in units of the relaxation timescale), mass segregation, velocity dispersion, and the energies of the binary population all show similar behaviour at different N.Comment: 9 pages, 8 figures, accepted for publication in MNRA

An exploration of local R&D spillovers in France

This paper is an attempt to assess the existence and magnitude of local research spillovers in France. We rely on the model of an extended production function (Cobb-Douglas and Translog) with both local and neighborhood R&D capital stocks. We estimate this model on 312 employment areas as of 1999, first for the whole economy, then separately for five large manufacturing industries. We find estimates of R&D capital elasticities with respect to productivity which are significant and plausible both within own-area and across neighboring areas, as well as within own-industry but not across different industries.Productivity, R&D, Local R&D Spillovers, Spatial Econometrics

Four-point function in general kinematics through geometrical splitting and reduction

It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the dimensionally-regulated one-loop four-point function in general kinematics is presented.Comment: 8 pages, 9 figures, contribution for proceedings of ACAT 2017 (Seattle, USA, August 21-25, 2017). arXiv admin note: substantial text overlap with arXiv:1605.0482

Excess entropy and energy feedback from within cluster cores up to r200_{200}

We estimate the "non-gravitational" entropy-injection profiles, $\Delta K$, and the resultant energy feedback profiles, $\Delta E$, of the intracluster medium for 17 clusters using their Planck SZ and ROSAT X-Ray observations, spanning a large radial range from $0.2r_{500}$ up to $r_{200}$. The feedback profiles are estimated by comparing the observed entropy, at fixed gas mass shells, with theoretical entropy profiles predicted from non-radiative hydrodynamic simulations. We include non-thermal pressure and gas clumping in our analysis. The inclusion of non-thermal pressure and clumping results in changing the estimates for $r_{500}$ and $r_{200}$ by 10\%-20\%. When clumpiness is not considered it leads to an under-estimation of $\Delta K\approx300$ keV cm$^2$ at $r_{500}$ and $\Delta K\approx1100$ keV cm$^2$ at $r_{200}$. On the other hand, neglecting non-thermal pressure results in an over-estimation of $\Delta K\approx 100$ keV cm$^2$ at $r_{500}$ and under-estimation of $\Delta K\approx450$ keV cm$^2$ at $r_{200}$. For the estimated feedback energy, we find that ignoring clumping leads to an under-estimation of energy per particle $\Delta E\approx1$ keV at $r_{500}$ and $\Delta E\approx1.5$ keV at $r_{200}$. Similarly, neglect of the non-thermal pressure results in an over-estimation of $\Delta E\approx0.5$ keV at $r_{500}$ and under-estimation of $\Delta E\approx0.25$ keV at $r_{200}$. We find entropy floor of $\Delta K\approx300$ keV cm$^2$ is ruled out at $\approx3\sigma$ throughout the entire radial range and $\Delta E\approx1$ keV at more than 3$\sigma$ beyond $r_{500}$, strongly constraining ICM pre-heating scenarios. We also demonstrate robustness of results w.r.t sample selection, X-Ray analysis procedures, entropy modeling etc.Comment: 17 pages, 15 figures, 5 tables, Accepted in MNRA

Little evidence for entropy and energy excess beyond r500r_{500} - An end to ICM preheating?

Non-gravitational feedback affects the nature of the intra-cluster medium (ICM). X-ray cooling of the ICM and in situ energy feedback from AGN's and SNe as well as {\it preheating} of the gas at epochs preceding the formation of clusters are proposed mechanisms for such feedback. While cooling and AGN feedbacks are dominant in cluster cores, the signatures of a preheated ICM are expected to be present even at large radii. To estimate the degree of preheating, with minimum confusion from AGN feedback/cooling, we study the excess entropy and non-gravitational energy profiles upto $r_{200}$ for a sample of 17 galaxy clusters using joint data sets of {\it Planck} SZ pressure and {\it ROSAT/PSPC} gas density profiles. The canonical value of preheating entropy floor of $\gtrsim 300$ keV cm$^2$, needed in order to match cluster scalings, is ruled out at $\approx 3\sigma$. We also show that the feedback energy of 1 keV/particle is ruled out at 5.2$\sigma$ beyond $r_{500}$. Our analysis takes both non-thermal pressure and clumping into account which can be important in outer regions. Our results based on the direct probe of the ICM in the outermost regions do not support any significant preheating.Comment: 6 pages, 4 figures, 1 table, Accepted in MNRAS Letter